If you know the components of a vector, what mathematical relationship can be used to find the magnitude of the vector?

Answers

Answer 1

Answer: You will always use Pythagoras theorem to find magnitude while given components of vector.
No matter if system that you are observing is 2D or 3D or higher (which is imaginery) pythagoras theorem will be applied.

Formula for determining magnitude is:
$M = √(x^ + y^2 + z^2 + ...)$

Number of turms inside square root you take depending on dimension of your system.

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Which of the following answers describes Kepler's laws?a. Planets orbit in elliptical patterns; the bigger the planet, the more gravitational pull; a planet's gravitational pull is stronger or weaker depending on its distance from the Sun.b. A planet's orbit covers equal distances in equal amounts of time; the speed of a planet's orbit depends on its distance from the Sun; the bigger the planet, the slower it moves.c. Planets orbit in elliptical patterns; a planet's orbit covers equal areas in equal amounts of time; planets' orbits are shorter or longer depending on their distance from the Sun.

A 15 kg box is sliding down an incline of 35 degrees. The incline has a coefficient of friction of 0.25. If the box starts at rest, how fast is it moving after it travels 3 meters?

Answers

The box has 3 forces acting on it:

• its own weight (magnitude w, pointing downward)

• the normal force of the incline on the box (mag. n, pointing upward perpendicular to the incline)

• friction (mag. f, opposing the box's slide down the incline and parallel to the incline)

Decompose each force into components acting parallel or perpendicular to the incline. (Consult the attached free body diagram.) The normal and friction forces are ready to be used, so that just leaves the weight. If we take the direction in which the box is sliding to be the positive parallel direction, then by Newton's second law, we have

• net parallel force:

∑ F = -f + w sin(35°) = m a

• net perpendicular force:

∑ F = n - w cos(35°) = 0

Solve the net perpendicular force equation for the normal force:

n = w cos(35°)

n = (15 kg) (9.8 m/s²) cos(35°)

n ≈ 120 N

Solve for the mag. of friction:

f = µn

f = 0.25 (120 N)

f ≈ 30 N

Solve the net parallel force equation for the acceleration:

-30 N + (15 kg) (9.8 m/s²) sin(35°) = (15 kg) a

a ≈ (54.3157 N) / (15 kg)

a ≈ 3.6 m/s²

Now solve for the block's speed v given that it starts at rest, with v₀ = 0, and slides down the incline a distance of ∆x = 3 m:

v² - v₀² = 2 a ∆x

v² = 2 (3.6 m/s²) (3 m)

v = √(21.7263 m²/s²)

v ≈ 4.7 m/s

Coal _____. is a renewable resource can easily be replenished is formed from plant remains is the least-polluting energy source

Answers

Coal . . . . .

-- is a renewable resource that can easily be replenished.
It happens by itself, and you don't even need to do anything,
but it takes several million years.

-- Is formed from plant remains, and

-- is perhaps the MOST polluting energy source.

There is only supposed to be one answer choice, so the correct answer is is formed from plant remains.

Tsunami waves have ?1. no crests
2. no troughs
3. long wavelengths
4. short wavelengths

Answers

I think it #3(not Sure) I think Its because of their long wavelengths that tsunamis behave as shallow-water waves.

The coordinates of a bird flying in the xy-plane are given by x(t)=αt and y(t)=3.0m−βt2, where α=2.4m/s and β=1.2m/s2.part a:Calculate the velocity vector of the bird as a function of time. Give your answer as a pair of components separated by a comma. For example, if you think the xcomponent is 3 and the y component is 4, then you should enter 3,4.part b:Calculate the acceleration vector of the bird as a function of time. Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4

Answers

α $=2.4 (m)/(s)$

β $=1.2 (m)/(s^2)$

$x(t)=at$

$y(t)=3-$ β $t^2$

$Vx(t)=$ α

$Vy(t)=-2$ β $t$

$vectorV=[$ α $;-2$ β $t]$

$ax(t)=0$

$ay(t)=-2$ β $t$

$vector a [0;-2$ β $t]$

Which one of the following lenses is a converging lens

Answers

Hi There! :)

Which one of the following lenses is a converging lens

Double-convex lens

The speed of a wave is determined by multiplying the wavelength by the frequency

Answers

Wellll . . . that's not a very easy way to do it. You'd still need
to figure out a way to measure the wavelength AND a way to
measure the frequency, so you won't find many engineers
actually trying to determine the wave speed by doing all of that.

But your statement is correct. The product of

(wavelength) times (frequency)

IS the speed of the wave.

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